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arXiv · 2505.24524

A new addition to the zoo of isolated symplectic singularities

Callum Berry
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Abstract

We give details of a new isolated symplectic singularity found in an affine chart in a crepant partial resolution of $\mathbb{C}^4/G_5$, which is 4-dimensional, isolated, and locally simply-connected. We distinguish the new singularity among all known such by the fact that the projective tangent cone at the singularity is non-reduced. We also find all 12 of its $\mathbb{Q}$-factorial terminalisations, in the process finding 24 for the quotient singularity $\mathbb{C}^4/G_5$.

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Callum Berry. 2025-05-30. A new addition to the zoo of isolated symplectic singularities. https://arxiv.org/abs/2505.24524

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